Systems and methods for digital video stabilization via constraint-based rotation smoothing

ABSTRACT

Systems and methods for digital video stabilization via constraint-based rotation smoothing are provided. Digital video data including a set of image frames having associated time stamps and a set of camera orientation data having associated time stamps may be provided. A smoothed set of camera orientation data may be generated by minimizing a rate of rotation between successive image frames while minimizing an amount of empty regions in a resulting set of smoothed image frames reoriented based on the smoothed set of camera orientation data.

PRIORITY

This application is a continuation of U.S. patent application Ser. No.14/101,252, filed on Dec. 9, 2013 entitled “SYSTEMS AND METHODS FORDIGITAL VIDEO STABILIZATION VIA CONSTRAINT-BASED ROTATION SMOOTHING”which claims the benefit of priority to U.S. Provisional PatentApplication No. 61/735,976, filed Dec. 11, 2012, the entireties of whichare hereby incorporated by reference.

FIELD OF THE INVENTION

The subject matter of the present disclosure relates to signalprocessing. More particularly, the present disclosure relates to systemsand methods for image and video processing.

BACKGROUND

Digital still cameras capable of capturing video have become widespreadin recent years. While the resolution and image quality of theseconsumer devices has improved up to the point where they rival digitalsingle-lens reflex cameras (DSLRs) in some settings, their video qualitymay still be significantly worse than that of film cameras. The reasonfor this gap in quality may be twofold. First, compared to film cameras,cell phones may be significantly lighter. As a result, hand-held videocapture on such devices may exhibit a greater amount of camera shake.Second, cell-phone cameras may have sensors that make use of a rollingshutter (RS). In an RS camera, each image row may be exposed at aslightly different time, which, combined with undampened camera motion,may result in a “wobble” in the output video.

Video stabilization is a family of techniques used to reducehigh-frequency frame-to-frame jitter produced by video camera shake. Inprofessional cameras, mechanical image stabilization (MIS) systems arecommonly used. For example, in an MIS system, the operator may wear aharness that separates the camera's motion from the operator's bodymotion. Other MIS systems stabilize the optics of the camera rather thanthe camera body itself. These systems may move the lens or sensor tocompensate for small pitch and yaw motions. These techniques work inreal time and do not require computation on the camera. However, theyare not suitable for mobile devices and inexpensive cameras, because oftheir price and size. Digital video stabilization systems may employfeature trackers to stabilize videos post-capture. However, thesesystems may be sensitive to noise (e.g., fast moving foreground objects)and require distinctive features for tracking. As a result, digitalstabilization based on feature tracking often breaks down, especially inadverse lighting conditions and excessive foreground motion. Inaddition, extracting and matching visual cues across frames can becomputationally expensive. Furthermore, the expense grows with theresolution of the video. In some instances, this may be too costly toperform video stabilization in real time. Consequently, such approachesare rarely employed in current digital cameras. Instead, manufacturerscan opt for more robust (and expensive) mechanical stabilizationsolutions for high-end DSLRs.

SUMMARY OF THE INVENTION

To stabilize digital video, computer implemented methods, systems, andcomputer readable media, in an embodiment, may provide digital videodata including a set of image frames having associated time stamps and aset of camera orientation data having associated time stamps. A smoothedset of camera orientation data may be generated by minimizing a rate ofrotation between successive image frames while minimizing an amount ofempty regions in a resulting set of smoothed image frames reorientedbased on the smoothed set of camera orientation data.

In an embodiment, the amount of empty regions in the resulting set ofsmoothed image frames may be minimized to zero.

In an embodiment, the amount of empty regions in the resulting set ofsmoothed image frames may be minimized below a threshold value.

In an embodiment, the set of image frames may be warped based on theassociated time stamps for the set of image frames and the smoothed setof camera orientation data to form a set of corrected image frames.

In an embodiment, the warping of the set of image frames based on theassociated time stamps for the set of image frames and the smoothed setof camera orientation data to form a set of corrected image frames mayinclude dividing an individual image frame into a plurality ofsubsections. Each subsection may have an associated time stamp andcamera orientation. The warping of the set of image frames based on theassociated time stamps for the set of image frames and the smoothed setof camera orientation data to form a set of corrected image frames mayinclude realigning each subsection based on the associated time stampand camera orientation to form an individual corrected image frame.

In an embodiment, the set of corrected image frames may be displayed asa video.

In an embodiment, the amount of empty regions in the resulting set ofsmoothed image frames may be minimized below a threshold value.

In an embodiment, the amount of empty regions below the threshold valuemay be inpainted.

In an embodiment, the set of camera orientation data having associatedtime stamps may be provided from a gyroscope of a handheld device.

In an embodiment, the set of image frames may be provided from a cameraof a handheld device.

In an embodiment, the set of camera orientation data having associatedtime stamps may be provided from a gyroscope of a handheld deviceincluding a mobile phone and a digital camera. The set of image framesmay be provided from the digital camera.

In an embodiment, the generating of the smoothed set of cameraorientation data includes an iterative optimization based on gradientdescent.

In an embodiment, the generating the smoothed set of camera orientationdata may include filtering based on a Gaussian filter.

In an embodiment, the generating of the smoothed set of cameraorientation data may include filtering based on a temporal derivative.

In an embodiment, the set of camera orientation data may includerotations without any translations.

In an embodiment, the set of camera orientation data may include vectorshaving both rotations and translations.

In an embodiment, the generating the smoothed set of camera orientationdata is performed by a social networking system.

In an embodiment, the set of image frames having associated time stampsand the set of camera orientation data having associated time stamps maybe uploaded to the social networking system by a user of the socialnetworking system.

Many other features and embodiments of the invention will be apparentfrom the accompanying drawings and from the following detaileddescription.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates an example pinhole camera model, according to anembodiment.

FIG. 2 illustrates a depiction of two example camera orientations andtheir corresponding image planes, according to an embodiment.

FIG. 3 illustrates a depiction of an example warped image captured by anRS camera and transformations to correct the image, according to anembodiment.

FIG. 4 illustrates an example digital video stabilization module,according to an embodiment.

FIG. 5 illustrates graphs of examples of input data and resulting dataafter smoothing, according to an embodiment.

FIG. 6 illustrates an example method for constraint-based smoothing,according to an embodiment.

FIG. 7 illustrates an example network diagram of a system for modifyinga set of image frames from a digital video to produce a stabilizeddigital video within a social networking system, according to anembodiment.

FIG. 8 illustrates an example computer system that may be used toimplement one or more of the embodiments described herein, according toan embodiment.

The figures depict various embodiments of the present invention forpurposes of illustration only, wherein the figures use like referencenumerals to identify like elements. One skilled in the art will readilyrecognize from the following discussion that alternative embodiments ofthe structures and methods illustrated in the figures may be employedwithout departing from the principles of the invention described herein.

DETAILED DESCRIPTION Digital Video Stabilization and Rolling ShutterCorrection using Gyroscopes

Rolling shutter correction is a technique for removing image warpingproduced by intra-frame camera motion. High-end cameras usecharge-coupled device (CCD) sensors, which have a global shutter (GS).In a GS camera, including many DSLRs, all pixels on the CCD sensor areread out and reset simultaneously. Therefore all pixels collect lightduring the same time interval. Consequently, camera motion during theexposure results in some amount of image blur on these devices. Incontrast, low-end cameras typically make use of complementary metaloxide semiconductor (CMOS) sensors. In particular, these sensors employa rolling shutter, where image rows are read out and reset sequentially.This approach may require less circuitry compared to CCD sensors and maymake CMOS sensors cheaper to manufacture. For that reason, CMOS sensorsare frequently used in cell phones, music players, and some low-endcamcorders. The sequential readout, however, means that each row isexposed during a slightly different time window. As a result, cameramotion during row readout will produce a warped image. Fast movingobjects will also appear distorted.

Image readout in an RS camera is typically in the millisecond range.Therefore, RS distortions are primarily caused by high-frequency cameramotions. MIS systems could, therefore, be used to stabilize the camera.While this approach removes rolling shutter warping, in practice theprice range and size of MIS systems make it not suitable for RS cameras.Some digital rolling shutter rectification techniques may correct RSartifacts in a single image, but require user input. In contrast, someembodiments of the present disclosure may correct RS artifacts forsingle images without requiring user input.

For video, rectifying RS in a sequence of frames using feature trackingto estimate the camera motion from the video may present problems. Oncethe camera motion is known during an RS exposure, it can be used torectify the frame. Since this approach relies on feature trackers, ithas the same disadvantages previously discussed in the case of videostabilization.

Digital video stabilization techniques may include cropping or zoominginput video frames. This may allow individual frames to be translated,rotated, or warped to counteract undesired deformations introduced byhand shake. The amount of cropping may determine how much leeway (or“wiggle room”) is available to remove these deformations. If, forexample, the frame is translated too far, empty regions (e.g., regionswhich have no pixel data) may be visible. Some embodiments of thepresent disclosure not only smooth out the camera motion bycounteracting hand shake, but may also do so while preventing emptyregions from showing up. It should be appreciated that other methods forproviding the leeway for stabilization, other than cropping or zooming,may also be implemented. For example, inpainting techniques may beimplemented to fill empty regions introduced by stabilization.Inpainting may be used in lieu of, or in addition to, cropping orzooming. For instance, in an embodiment, a function may be implementedto determine whether a given deformation results in a frame with allpixels set (whether by inpainting, zooming, cropping, etc.) tosatisfaction or not.

Systems and methods are provided for digitally stabilizing videos bycomputing smooth camera rotations that satisfy empty-region preventionconstraints. This may enable maximally smooth camera rotations to beproduced for a given crop or zoom factor.

The digital video stabilization process may begin, for example, withvideo being captured by a camera or device including a camera, such as amobile phone, tablet, watch, wearable gear, etc. The video may include anumber of successive image frames that are captured. The video may beshaky due to the device's size and weight. The rolling shutter used bysensors in the camera may produce warping in the output image frames.Gyroscopes may be used to measure the camera's motions (e.g., rotations)during video capture. The measured camera motion may be used tostabilize the video and to rectify the rolling shutter to result in thestabilized video having output frames with corrected images.

Techniques of the present disclosure may improve video quality of RScameras. In an embodiment, microelectromechanical systems (MEMS)gyroscopes are implemented to measure camera rotations. Other gyroscopesand motion sensing devices may also be implemented. The gyroscopicmeasurements may be used to perform video stabilization (e.g.,inter-frame motion compensation) and rolling shutter correction (e.g.,intra-frame motion compensation). This approach may be bothcomputationally inexpensive and robust, which may make it particularlysuitable for real-time implementations on mobile platforms for instance.

Systems and methods based on a unified model of a rotating camera and arolling shutter may utilize the model to compute a warp thatsimultaneously performs rolling shutter correction and videostabilization. Optimization techniques may be provided thatautomatically calibrate the gyroscope and camera. This may permit therecovery of unknown parameters, such as gyroscope drift and delay, aswell as the camera's focal length and rolling shutter speed, from asingle video and gyroscopic capture. As a result, any combination ofgyroscope and camera hardware may be calibrated without the need for aspecialized laboratory setup. A device including the camera may alsoinclude a motion sensing device, such as a gyroscope. For example, manysmartphones have cameras and motion sensing devices, such as gyroscopesand accelerometers. In this way, real-time video stabilization androlling shutter correction may be provided without requiring the use offeature trackers or MIS systems. Furthermore, inexpensive MEMSgyroscopes may be implemented to measure camera motion directly.Inertial measurement units (IMUs) may be used for image de-blurring andfor aiding a KLT feature tracker

Measuring camera motion using motion sensing devices, such asgyroscopes, permits digital video stabilization and RS rectification tobe performed with high computational efficiency. This approach may berobust even under poor lighting or substantial foreground motion,because the video's content is not used for motion estimation.Furthermore, as stated above, many camera-enabled mobile phones arealready equipped with gyroscopes or other motion sensing devices.Compared to MIS systems, MEMS gyroscopes may be significantly lessinexpensive, more versatile, and less bulky.

In an embodiment, video stabilization may proceed in three stages:camera motion estimation, motion smoothing, and image warping. Rollingshutter rectification may proceed in a similar manner, except the actualcamera motion may be used for the warping computation rather than thesmoothed motion. As will be discussed in further detail herein, bothvideo stabilization and rolling shutter correction may be performed inone warping computation under a unified framework.

In an embodiment, camera motion may be modeled in terms of rotationsonly. It should be appreciated that translations may be measured inaddition to, or in place of, rotations in other embodiments. In someinstances, translations may be difficult to measure accurately usingIMUs for example. Moreover, accelerometer data may require beingintegrated twice to obtain translations. In contrast, gyroscopes measurethe rate of rotation. Therefore, gyroscopic data may require only asingle integration to obtain the camera's orientation. As a result,translation measurements may be significantly less accurate thanorientation measurements in some instances. Furthermore, translationmeasurements may be complicated by objects at different depths moving bydifferent amounts. In an embodiment, stereo or feature-based structurefrom motion (SfM) algorithms may be implemented to obtain depthinformation. Warping frames in order to remove translations may beperformed in some embodiments, but may be complicated by parallax andocclusions.

Modeling camera translations in systems may present issues. For example,an optimizer may fall into a local minimum while attempting toreconstruct translations from a feature tracker. An algorithm may assumethat the camera is imaging a purely planar scene (e.g., constant depth).Therefore, translation reconstruction may be complicated due tounmodeled parallax in the video.

Embodiments modeling camera rotation only in terms of rotations, orprimarily in terms of rotations, may minimize the problems encounteredwith translations. Camera shake and rolling shutter warping occurprimarily from rotations since translations attenuate quickly withincreasing depth, and objects are typically sufficiently far away fromthe lens that translational camera jitter does not produce noticeablemotion in the image.

Example Camera Model

In an embodiment, a rotational rolling shutter camera model that isbased on a pinhole camera model is provided. FIG. 1 illustrates anexample pinhole camera model 101, according to an embodiment. A ray froma camera center c to a point x in the scene will intersect the imageplane at point x. Therefore the projection of the world onto the imageplane depends on the camera's center c, the focal length f, and thelocation of the camera's axis (o_(x), o_(y)) in the image plane. In apinhole camera the relationship between image point x in homogeneouscoordinates and the corresponding point X in 3D world coordinates may bespecified by example equation (1).

x=KX, and X=λK ⁻¹ x   (1)

Here, λ is an unknown scaling factor and K is the intrinsic camera. K⁻¹may be specified by example equation (2).

$\begin{matrix}{K^{- 1} = \begin{pmatrix}1 & 0 & {- o_{x}} \\0 & 1 & {- o_{y}} \\0 & 0 & f\end{pmatrix}} & (2)\end{matrix}$

(o_(x), o_(y)) is the origin of the camera axis in the image plane and fis the focal length. The camera's focal length is an unknown that may berecovered. The camera may be assumed to have square pixels and the upperdiagonal entries set to 1. However, other embodiments may extend thismodel to take into account non-square pixels or other opticaldistortions.

Warping may occur from high-frequency camera rotations. For example,high-frequency camera rotations while the shutter is rolling from top tobottom may cause the output image to appear warped. This warped imagemay be modeled mathematically.

The world origin may be set to the camera origin. The camera motion maythen be described in terms of its orientation R(t) at time t. Thus, forany scene point X, the corresponding image point x at time t may begiven by example equation (3).

x=KR(t)X   (3)

The rotation matrices R(t)ε SO(3) may be computed by compounding thechanges in camera angle Δθ(t). The spherical linear interpolation(SLERP) of quaternions may be used in order to interpolate the cameraorientation smoothly and to avoid gimbal lock. The change in anglebetween gyroscope samples may be sufficiently small that Euler angleswork as well as rotation quaternions. Δθ(t) may be obtained directlyfrom gyroscope measured rates of rotation ω(t), as specified in thefollowing example equation (4).

Δθ(t)=(ω(t+t _(d))+ω_(d))*Δt   (4)

ω_(d) is the gyroscope drift and t_(d) is the delay between thegryoscope and frame sample timestamps. These parameters are additionalunknowns in that model that may also be recovered.

Rolling shutter may also be introduced into the camera model. In an RScamera, each image row is exposed at a slightly different time. Camerarotations during this exposure may, therefore, determine the warping ofthe image. Translational camera jitter during rolling shutter exposuredoes not significantly impact image warping because objects aretypically far away from the lens. For example, if the camera sways fromside to side while the shutter is rolling, then the output image will bewarped as shown in FIG. 3. The time at which point x was imaged in framei depends on how far down the frame it is. It may be determined that xwas imaged at time t(i, y), as specified by the example equation (5).

t(i,y)=t _(i) +t _(s) *y/h, where x=(x,y,1)^(T)   (5)

y is the image row corresponding to point x. h is the total number ofrows in the frame. t_(i) is the timestamp of the i-th frame. The t_(s)term indicates that the farther down in a frame, the longer it took forthe rolling shutter to get to that row. Hence, t_(s) is the time ittakes to read out a full frame going row by row from top to bottom. Anegative t_(s) value would indicate a rolling shutter that goes frombottom to top. Automatically recovering the sign and value of t_(s) isdescribed in further detail herein.

The relationship between image points in a pair of frames for twodifferent camera orientations may be derived. FIG. 2 illustrates agraphical representation of two camera orientations and theircorresponding image planes, according to an embodiment. Graphicalrepresentation 201 includes two camera orientations 202 and 203. Cameraorientation 202 includes image plane i. Camera orientation 203 includesimage plane j. An image of scene point X appears in the two frames wherethe ray 211 intersects the image planes i and j. For a scene point X,the projected points x_(i) and x_(j) in the image plane of two frames iand j, respectively, may be specified by the following example equations(6).

x _(i) =KR(t(i,y _(i)))X, and x _(j) =KR(t(j,y _(j)))X   (6)

If these equations are rearranged and if X is substituted for, a mappingof all points in frame i to all points in frame j is obtained, asspecified by example equation (7).

x _(j) =KR(t(j,y _(j)))R ^(T)(t(i,y _(i)))K ⁻¹ x _(i)   (7)

While the relationship between two frames have been described inrelation to the same video, in other embodiments, the frames may bemapped from one camera that rotates according to R(t) to another camerathat rotates according to R′(t). In an embodiment, both camera centersmay be assumed to be at the origin. The warping matrix W that mapspoints from one camera to the other may be specified according to thefollowing example equation (8).

W(t ₁ ,t ₂)=KR′(t ₁)R ^(T)(t ₂)K ⁻¹   (8)

Equation 7 may now be specified more compactly according to thefollowing example equation (9).

x _(j) =W(t(j,y _(j)),t(i,y _(i)))x _(i), where R′=R   (9)

W depends on both image rows y_(i) and y_(j) of image points x_(i) andx_(j), respectively. This warping matrix may be used to match points inframe i to corresponding points in frame j, while taking the effects ofthe rolling shutter into account in both frames.

This formulation of a warping matrix provides for rolling shuttercorrection and video stabilization. A synthetic camera may be createdthat has a smooth motion and a global shutter. This camera's motion maybe computed by applying a Gaussian low-pass filter, for example, to theinput camera's motion, which results in a new set of rotations R′. Therolling shutter duration t_(s) for the synthetic camera may be set to 0as for a global shutter. W(t_(i), t(i, y_(i))) may then be computed ateach image row y_(i) of the current frame i, and the warp may be appliedto that row. The first term of W may now only depend on the frame timet_(i). This operation may map all input frames onto the syntheticcamera, and as a result, simultaneously remove rolling shutter warpingand video shake.

In certain embodiments, W(t_(i), t(i, y_(i))) is not computed for eachimage row y_(i). Instead, the input image may be subdivided and the warpcomputed at each vertical subdivision. FIG. 3 illustrates an exampletransformation to correct warp, according to an embodiment. Warped inputimage frame 301 shows a subdivided warped image that was captured by anRS camera. The warp is computed at each vertical subdivision, as shownin image frame 311. Image frame 311 shows a piecewise linearapproximation of non-linear warping. As shown by resulting image frame316, various numbers of subdivisions may be sufficient to eliminateartifacts. For example, in an embodiment, 10 subdivisions may besufficient to eliminate visual artifacts. A warped mesh from the inputimage was created that is a piecewise linear approximation of thenon-linear warp. While ten subdivisions may be sufficient to remove anyvisible RS artifacts, other embodiments may include a different numberof subdivisions. The sampling approach may be referred to as inverseinterpolation. Inverse interpolation may be easy to implement on agraphical processing unit (GPU) using vertex shaders. The GPU's fragmentshader may take care of resampling the mesh-warped image using bilinearinterpolation. RS warping in actual videos may not be strong enough toproduce aliasing artifacts due to bilinear inverse interpolation. As aresult, inverse interpolation may work well in practice. Rolling shuttercorrection using global image warps may assume that camera rotation ismore or less constant during rolling shutter exposure. A linearapproximation may fail to rectify the rolling shutter, as shown by imageframe 306 in FIG. 3.

Camera and Gyroscope Calibration

Calibration techniques are provided for recovering the unknown cameraand gyroscope parameters described herein. The calibration may enablethe computation of W directly from the gyroscope data. The unknownparameters in the model described herein may include: the focal lengthof the camera f, the duration of the rolling shutter t_(s), the delaybetween the gyroscope and frame sample timestamps t_(d), and thegyroscope drift w_(d).

In some instances, one or more of these parameters, such as the camera'sfocal length f, may be specified by the manufacturer. In some instances,these parameters may be measured experimentally. For example, a quicklyflashing display may be used to measure the rolling shutter durationt_(s). However, these techniques may tend to be imprecise and errorprone. These techniques may also be tedious. The duration of the rollingshutter may typically be in the millisecond range. As a result, a smallmisalignment in t_(d) or t_(s) may cause rolling shutter rectificationto fail.

In an embodiment, these parameters may be estimated from a single videoand gyroscope capture. For example, the user may be record a video and agyroscope trace while standing still and shaking the camera whilepointing at a stationary object, such as a building. The duration of theclip may vary in different embodiments. In an embodiment, a short clip(e.g., ten seconds or less in duration) may be sufficient to estimateall the unknown parameters. This calibration step may only need to bedone once for each camera and gyroscope arrangement.

In an embodiment, matching points are identified in consecutive videoframes. The matching points may be identified using, for example, thescale invariant feature transform (SIFT). Outliers may be discardedusing, for example, random sample consensus (RANSAC). The result may bea set of point correspondences x_(i) and x_(j) for all neighboringframes in the captured video. Given this ground truth, calibration maybe formulated as an optimization problem where the mean-squaredre-projection error of all point correspondences may be minimized. Thisis specified in the following example equation (10).

$\begin{matrix}{J = {\sum\limits_{({i,j})}\; {{x_{j} - {{W\left( {{t\left( {j,y_{j}} \right)},{t\left( {i,y_{i}} \right)}} \right)}x_{i}}}}^{2}}} & (10)\end{matrix}$

A number of non-linear optimizers may be used to minimize the objectivefunction. Coordinate descent by direct objective function evaluation mayconverge quickly, and is implemented in one embodiment. Each time a stepis taken where the objective function J does not decrease; the stepdirection is reversed and the step size of the corresponding parameteris decreased. The algorithm may terminate when the step size for allparameters drops below a desired threshold, such as when a targetprecision is achieved. The convergence may occur quickly in someinstances. For example, in one embodiment, the convergence may occur in2 seconds or less for a calibration video of about 10 seconds induration.

In an embodiment, the optimization may be initialized by setting thefocal length such that the camera has a field of view of 45°. All otherparameters may be set to 0. With these initial conditions, the optimizermay converge to the correct solution for the dataset. More generally,falling into a local minimum (e.g., when the delay between the gyroscopeand frame timestamps is large) may be avoided by restarting thecoordinate descent algorithm for a range of plausible parameters, andselecting the best solution. The average re-projection error forcorrectly recovered parameters may be, for example, around 1 pixel.

An additional unknown in the model may be the relative orientation ofthe gyroscope to the camera. For example, rotations about the gyro'sy-axis may correspond to rotations about the camera's x-axis.

To discover the gyroscope orientation, the 3 rotation axes may bepermuted and the optimizer may be run for each permutation. Thepermutation that minimizes the objective best may correspond to thecamera's axis ordering. The re-projection error may be significantlylarger for incorrect permutations. Therefore, this method may work wellin practice.

While it has been assumed that the camera has a vertical rollingshutter, the RS model may be easily modified to work for image columnsinstead of rows. Finding the minimum re-projection error for both casesmay indicate whether the camera has a horizontal or vertical rollingshutter.

Finally, the results achieved by calibration may be demonstrated byanalyzing the video and gyroscope signals before and after calibration.Assuming rotations between consecutive frames are small, thetranslations in the image may be approximately computed from rotationsas specified in the following example equation (11).

$\begin{matrix}{{{\overset{.}{x}(t)} \approx {f*{\hat{\omega}\left( {t + t_{d}} \right)}}},{{where}\mspace{14mu} \left\{ \begin{matrix}{\overset{.}{x} = \left( {\overset{.}{x},\overset{.}{y}} \right)^{T}} \\{\hat{\omega} = \left( {\omega_{y},\omega_{x}} \right)^{T}}\end{matrix} \right.}} & (11)\end{matrix}$

Equation (11) assumes there are no effects due to rolling shutter (e.g.,t_(s)=0), and rotations about the z-axis (e.g., ω_(z)) may be ignored.{dot over (x)} is the average rate of translation along x and y for allpoint correspondences in consecutive frames. If the optimizer convergedto the correct focal length f and gyroscope delay t_(d), then the twosignals should align. Before calibration, the amplitudes of the signalsx and f*ωy(t+t_(d)) do not match because the initial estimate for f istoo low. The signals may be shifted when t_(d) is initialized to 0.After calibration, the signals may be well aligned because accuratefocal length and gyroscope delay have been recovered. Precisegyroscopes, such as MEMS gyroscopes, enable the gyroscope data to matchthe image motions, resulting in the improved video stabilization androlling shutter correction.

Constraint-Based Rotation Smoothing

In some aspects of the present disclosure, system and methods may beprovided for computing an optimally smooth camera motion under theconstraint that empty regions are not visible, or below a minimumthreshold value. FIG. 4 illustrates an example digital videostabilization module, according to an embodiment. Digital videostabilization module 400 is shown including an input module 401, asmoothing module 402, and a warping module 403.

Input module 401 may provide inputs to be stabilized the smoothingmodule 402 and the warping module 405. Input module 401 may receive theinputs associated with the video that is to be stabilized. For example,inputs may include a set of N frames F_(i), corresponding times t_(i)for the N frames F_(i), and camera orientations θ_(i), where i={1 . . .N}.

Smoothing module 402 computes a set of new smoothed camera orientationsφ_(i), such that a constraint function f(φ, t) is satisfied. Smoothingmodule 402 may include rate of rotation module 403 and constraintdetermination module 404.

Rate of rotation module 403 computes the rate of rotation to ensure asufficiently small rate of rotation is maintained for the generation ofsmooth camera orientations. Constraint determination module 404determines whether a constraint is met for target orientations φ_(i) attime t_(i). For example, in one embodiment, the constraint functionf(φ,t) may return 1 or 0 depending on whether empty regions are visibleor not, respectively, given a target orientation φ_(i) at time t_(i).

For example, the constraint determination module 404 may determinewhether a minimal amount of empty regions (e.g., below a thresholdamount) are produced in successive image frames. If the amount of emptyregions falls below the threshold amount, then the constraint is met(e.g., the amount of empty regions does not exceed the thresholdamount), and the target orientation φ and its corresponding time t maybe used to generate a smooth orientation that has a sufficiently smallrate of rotation that does not generate an amount of empty spaces abovea threshold value. If the constraint is not met (e.g., the amount ofempty regions exceeds the threshold amount), then the correspondingtarget orientation φ may be adjusted to maintain a sufficiently smallrate of rotation while satisfying the constraint. In an embodiment, thethreshold amount of empty regions is zero. In another embodiment, thethreshold amount of empty regions is approximately zero or a negligiblevalue that is determined to be undetectable by the human eye. In yetanother embodiment, the threshold amount of empty regions is a valuethat prevents cropping, zooming, or inpainting to be used effectively,such as to eliminate all empty regions, or approximately all emptyregions. In other embodiments, the threshold amount of empty regions maybe set as desired based on the application and level of tolerance.

Warping module 405 generates warped frames based on the set of newsmoothed camera orientations φ_(i) computed by the smoothing module 402.For example, the warping module 405 may implement a warping functiong(F, φ, t) that takes as input a frame F, a smoothed orientation φ andits corresponding time t, and generates a warped frame F′. Given thesmoothly varying φ_(i) over t_(i) as output by the smoothing module 402,and appropriate choices of functions f and g, the resulting warpedframes F′_(i) will compose a stabilized output video. The function f maydepend on the choice of warping function g, and may simply indicatewhether, after applying the warping function g, empty regions would bevisible in the frame or not.

The specific warping function implemented may vary in differentembodiments. Different warping functions may be appropriate for variouscameras or desired approximations. For example, the warping functionimplemented may be based on whether a camera has a rolling shutter andminor lens aberrations or whether it has a global shutter. For instance,in one embodiment, for cameras with a global shutter, a homographywarping function may be implemented. Other approximations, such asaffine transformations, or a rotation plus a translation in the frame'simage space may be implemented.

In an embodiment, the θ_(i) input are rotations in the SO(3) group.There are a variety of ways to represent rotations, such as by rotationmatrixes and quaternions. Representations that lie in SO(3) may beconverted into a representation that facilitates smooth interpolation,such as quaternions rather than Euler angles. The θ_(i) rotations may becomputed from an image-based feature tracker, for example, or bydirectly measuring and integrating gyroscope readings. Any other methodthat produces accurate estimates of the camera's orientation may beimplemented in other embodiments.

While φ has been described in terms of camera rotations, in otherembodiments θ may include a vector that holds both rotations andtranslations of the camera in 3D space. For instance, vectors thatinclude both rotations and translations may be produced by a structurefrom motion algorithm. In an embodiment, θ may include translations orrotations in the frame's image space, or other less accurate butpotentially computationally cheaper approximations. As long as θ can besmoothly interpolated and the resulting φ can be input to acorresponding f and g function, the digital video stabilization may beachieved.

The phrase “smooth camera motion” may be used herein to refer to smallchanges in the rate of rotation. This is distinguished from smallchanges in rotation of neighboring frames. Small changes in the rate ofrotation may produce orientations that ease in and out of imposedconstraints over time. Small changes in rotation of neighboring framesinterpolates to and from the constraints while producing discontinuitiesin orientation derivatives at the time where the constraint is enforced.

The constraint-based rotation smoothing may include an optimization thatincludes minimizing an energy function based on rate of rotation and theconstraint.

In an embodiment, the energy function, J, to be minimized may bespecified by the following example equation (12).

$\begin{matrix}{J = {{\sum\limits_{i = 2}^{N - 1}\; {{{\frac{\varphi_{i + 1} - \varphi_{i}}{t_{i + 1} - t_{i}} - \frac{\varphi_{i} - \varphi_{i - 1}}{t_{i} - t_{i - 1}}}}^{2}{s.t.\mspace{14mu} {f\left( {\varphi_{i},t_{i}} \right)}}}} = {0{\forall i}}}} & (12)\end{matrix}$

The rotations φ may be represented as unit quaternions (also known asversors). Furthermore, the hard constraint may be replaced with a softconstraint, as specified in the following example equation (13).

$\begin{matrix}{J = {{\sum\limits_{i = 2}^{N - 1}\; {{\frac{\varphi_{i + 1} - \varphi_{i}}{t_{i + 1} - t_{i}} - \frac{\varphi_{i} - \varphi_{i - 1}}{t_{i} - t_{i - 1}}}}^{2}} + {\lambda {\sum\limits_{i = 1}^{N}\; {f\left( {\varphi_{i},t_{i}} \right)}}}}} & (13)\end{matrix}$

λ may determine how strongly the f constraint is enforced. For example,setting λ to infinity may ensure that no empty regions are visible,assuming the constraints may be satisfied.

A variety of optimization algorithms may be used to minimize the energyfunction J in either the form shown in example equation (12) or (13). Inan embodiment, an iterative algorithm based on gradient descent ofexample equation (12) is implemented, where the constraint may beenforced at each iteration. In an embodiment, the frames may be equallyspaced temporally, such as a camera that records at a specific number offrames per second. With equally spaced frames, the denominator may beassumed to be constant and may then be taken out of the sum. Thederivative may then specified by the following example equation (14).

$\begin{matrix}{{\frac{\partial J}{\partial\varphi_{i}} = {C\left( {\varphi_{i + 2} - {4\; \varphi_{i + 1}} + {6\; \varphi_{i}} - {4\; \varphi_{i - 1}} + \varphi_{i - 2}} \right)}},} & (14)\end{matrix}$

C may be a constant that controls the magnitude of the gradient. In someembodiments, this may be picked automatically by some forms of gradientdescent, such as momentum-based methods. In other embodiments, this maybe set as desired to control the rate of descent in plain gradientdescent. An example value may be, for instance, C=2/(Δt)². Equation (14)may be specified more compactly by the following example equation (15).

$\begin{matrix}{{\frac{\partial J}{\partial\varphi_{i}} = {{CK}\; \Phi_{i}}},{{{where}\mspace{14mu} K} = \begin{bmatrix}1 \\{- 4} \\6 \\{- 4} \\1\end{bmatrix}^{T}},{{{and}\mspace{14mu} \Phi_{i}} = \begin{bmatrix}\varphi_{i + 2}^{T} \\\varphi_{i + 1}^{T} \\\varphi_{i}^{T} \\\varphi_{i - 1}^{T} \\\varphi_{i - 2}^{T}\end{bmatrix}}} & (15)\end{matrix}$

The kernel K may be a Laplacian of Gaussian (LoG) filter. The LoG filtermay be approximated with a Difference of Gaussians (DoG) or Differenceof Boxes (DoB) filter. The kernel K may also be adjusted by convolving aLoG filter with a Gaussian filter. This may control how gradually therate of rotation should change (or the amount of easing in and out ofconstraints). The choices of the LoG/DoG/DoB and/or Gaussian filters mayaffect the coefficients and size of kernel K, but as long as the kernelcomputes a form of a temporal derivative, the optimized orientations mayexhibit some form of easing in and out of the constraints.

In an embodiment, the applying of the kernel to the quaternions is doinglinear weighting of the 4D vectors. In theory, interpolating quaternionsusing spherical linear interpolation (slerp) may be an accurate method.For small changes in angles, linear interpolation plus a normalizationof the resulting quaternion (lerp) at each iteration is sufficient toproduce sufficiently accurate results. Such results may be achievedbecause sin(θ)≈θ when θ is small. The change in angle induced byhandshake (e.g., changes that are to be rectified) are typically notlarge. Furthermore, reasonable levels of cropping, zooming, orinpainting factors may not leave much leeway. Only small angles may notproduce empty regions. Thus, the angle induced by handshake betweenquaternions of consecutive orientations may not be large in practice,and the approximation may be both accurate and computationallyefficient. Furthermore, for rapid camera rotations (e.g., the userquickly panning left), the constraint function f may dominate theresulting orientations. Thus, any inaccuracies from lerp may not benoticeable.

In an embodiment, the constraint-based rotation smoothing may bespecified in terms of the following example algorithm (1).

Algorithm 1 Constraint-Based Rotation Smoothing for i = 1..N do φ_(i) ←θ_(i) end for for j = 1..numiter do for i = 3..(N − 2) do if f(n(φ_(i) −CKΦ_(i)), t_(i)) = 0 then φ_(i) ← n(φ_(i) − CKΦ_(i)) end if end for endforφ_(i) may be precomputed in the outer loop, such that it does not changein the inner loop. The number of iterations, “numiter”, may be setsufficiently high to result in smooth rotations. The resulting φ_(i) maythen be fed into g to produce a stabilized output video.

n(φ) is the normalization step in lerp and may be defined as:n(φ)=φ/∥φ∥. The indexing i in algorithm 1 is selected such that φ_(i) isvalid, and therefore may depend on the size of the kernel K. In thisexample, the rotations at the boundaries may be held fixed. In otherembodiments, the boundary may be extended via extrapolation, allowingfor the entire set of orientations to be iterated over duringoptimization. The entire set of orientations may be specified as thefollowing set.

{φ_(i)}_(i=1) ^(N)

FIG. 5 illustrates graphs of examples of input data and resulting dataafter smoothing, according to an embodiment. The top graph includesinput data 502 plotted over time with constraints 503 denoted bycircles. The bottom graph includes resulting data 504, includingconstraints 503, that resulted from the input data 502 being smoothed inaccordance with the constraint-based rotation smoothing techniquesdescribed herein. For example, the resulting data 504 may be smoothed byenforcing the rate of rotation (or derivative) to be small (or below athreshold value) while ensuring that the constraint (e.g., a thresholdamount of empty regions are not produced in successive image frames) ismet. Small changes in the rate of rotation may produce orientations thatease in and out of imposed constraints over time. The resulting data 504eases in and out of the constraints 503. On the other hand, the middlegraph includes resulting data 506, including constraints 503, thatresulted from an attempted smoothing of the input data 502 by enforcingthe change in orientation of neighboring frames to be small. Smallchanges in rotation of neighboring frames interpolates to and from theconstraints while producing discontinuities in orientation derivativesat the time where the constraint is enforced. As shown, the resultingdata 506 includes discontinuities in the derivative at the constraints503.

FIG. 6 illustrates an example method for constraint-based smoothing,according to an embodiment. At block 601 of method 600, video data isreceived. The video data may include a set of image frames havingassociated time stamps. In an embodiment, block 601 may be performed byinput module 701 of FIG. 4.

At block 603, camera orientation data having associated time stamps arereceived. For example, the device including the camera may also includean orientation sensor, such as a gyroscope, accelerometer, etc., thatgenerates camera orientation data that tracks the orientation of thecamera during the capture of the video. The camera orientation data mayinclude associated time stamps to link or otherwise associate the cameraorientation data to the set of images in the video data. In someinstances, the camera orientation data may be received at the same timeas the video data, such as together with the video data. In anembodiment, block 602 may be performed by input module 701 of FIG. 4.

In one embodiment, blocks 601 and 603 may be performed by the devicehaving the camera (e.g., smartphone or other handheld device) that isused to capture the video. For example, the video data and cameraorientation data may be received upon capture of the video. In anotherembodiment, blocks 601 and 603 may be performed by a separate device(e.g., computer) that subsequently receives the video data captured bythe device including the camera (e.g., smartphone). For example, thevideo data and camera orientation data may be transmitted or uploaded toa separate device from the device including the camera and orientationsensor, such as a smartphone with camera.

At block 605, a set of smoothed camera orientation data is generated byminimizing the rate of rotation between successive images frames whileminimizing (or limiting) the amount of resulting empty regions in aresulting set of smoothed image frames. The resulting set of smoothedimage frames are reoriented based on the smoothed set of cameraorientation data.

In an embodiment, the set of smoothed camera orientation data isgenerated by minimizing either equations (12) or (13) described herein.In an embodiment, an iterative algorithm based on gradient descent ofexample equation (12) is implemented, where the constraint may beenforced at each iteration.

At block 607, the set of image frames are warped to form a set ofcorrected image frames. The set of image frames may be warped based onthe associated time stamps for the set of image frames and the smoothedset of camera orientation data. In an embodiment, an individual imageframe may be divided into a plurality of subsections, with eachsubsection having an associated time stamp and camera orientation. Eachsubsection may be realigned based on the associated time stamp andcamera orientation to form an individual corrected image frame.

Reducing Visibility of Motionblur Artifacts

Digital video stabilization of video taken in low light often producesstrange motion blur artifacts. This may occur because motion blur looksstrange when the motion (e.g., handshake) that caused it is removed. Insome instances, it may be necessary to leave just enough of thehandshake in the stabilized video to explain the motion trails. If thereis a clear horizontal motion trail in a frame, it may be necessary forthe orientation to change horizontally according to that trail in orderto for the trail to make sense. If there is no horizontal motion, thenthat trail may appear to pop in and out for no reason in the stabilizedvideo, which can cause visible motion blur artifacts.

In an embodiment, the change in orientation Δθ_(i) that occurred whilethe camera's shutter was open is computed according to the followingexample equation (16).

Δθ_(i)=θ(t _(i) ^(s))−θ(t _(i) ^(s) +e _(i))   (16)

t_(i) ^(s) may represent the time at which the shutter opened for frameF_(i). e_(i) is the frame's exposure duration. θ(t) is the camera'sorientation at time t, which may be computed by interpolating over thefollowing expression.

{θ_(i) ,t _(i)}_(i=1) ^(N)

In the example described above for digital video stabilization androlling shutter correction using gyroscopes, Δθ_(i) may also be computeddirectly from the gyroscope readings by only integrating over the periodwhere the shutter is open. The sum inside equation (1) or equation (2)may be modified as specified in the following example equation (17).

$\begin{matrix}{\sum\limits_{i = 2}^{N - 1}\; {{\frac{\varphi_{i + 1} - \varphi_{i}}{t_{i + 1} - t_{i}} - \frac{\varphi_{i} - \varphi_{i - 1}}{t_{i} - t_{i - 1}} - \left( {{\Delta \; \theta_{i}} - {\Delta \; \theta_{i - 1}}} \right)}}^{2}} & (17)\end{matrix}$

Equation (17) assumes that t_(i) ^(s)≧t_(i) and t_(i)^(s)+e_(i)≦t_(i+1). The shutter does not open before the timestamp ofthe frame, and closes prior to the start of the next frame. In anotherembodiment, the input time stamps may be calculated differently (e.g.,t_(i) is the time when the shutter closed) and a preprocessing step maybe added to adjust the timestamps to meet the requirements.

In the embodiment described above, changes in orientation that leftmotion trails in the frames are preserved. In another embodiment, anapproximation may be implemented as specified by the following exampleequation (18).

$\begin{matrix}{{\sum\limits_{i = 2}^{N - 1}\; {{\frac{\varphi_{i + 1} - \varphi_{i}}{t_{i + 1} - t_{i}} - \frac{\varphi_{i} - \varphi_{i - 1}}{t_{i} - t_{i - 1}}}}^{2}} + {\gamma {\sum\limits_{i = 1}^{N - 1}{{\frac{\varphi_{i + 1} - \varphi_{i}}{t_{i + 1} - t_{i}} - {\Delta \; \theta_{i}}}}^{2}}}} & (18)\end{matrix}$

The approximation in equation (18) may attempt to optimize φi such thatorientation changes fall along motion trails Δθ_(i). The γ scalingfactor may control the tradeoff between smoothness and how closely themotion trails should be followed.

Selecting a Good Zoom Factor

If, for example, a tolerable zoom factor (or crop factor, inpaintingfactor, or any other measure applicable to the algorithm used to provideleeway for digital video stabilization) is between 1 and 1.25×. For agiven video, it may be desirable to determine the smallest zoom factorthat will provide enough leeway to produce smooth camera motions. In anembodiment, the smoothness of the resulting camera motion may bemeasured by the following example equation (19).

$\begin{matrix}{q = {\frac{1}{N - 2}{\sum\limits_{i = 2}^{N - 1}\; {f\left( {{n\left( {\varphi_{i} - {{CK}\; \Phi_{i}}} \right)},t_{i}} \right)}}}} & (19)\end{matrix}$

In equation (19), q measures how frequently the empty region constraintis enforced. For example, a value of q=0.1 may mean that on average f isenforced every 10 frames in order to prevent empty regions from showingthrough. If, for example, a spacing of 20 frames is desired for easingin and out of constraints, then a good value may be q=0.05.

To find the zoom factor z′ that provides a desired q′ value, algorithm 1may be solved for a range of zoom factors (say: zε[1, 1.05, 1.1, 1.15,1.2, 1.25]). Given a zoom factor z and the resulting φ_(i)'s obtained byrunning algorithm 1, the resulting q value may be computed from equation(19). The zoom factor that provided the closest q to q′ may then beselected. In another embodiment, the zoom factor z′ may be found bylinearly interpolating the resulting dataset (q, z) at q′. The (q, z)lookup table for typical hand-held recordings may also be precomputedand q′ estimated from the median or mean rate of rotation. This approachmay be less accurate for a particular video, but it may be fasterbecause it doesn't require running the optimization algorithm multipletimes.

Improving Computational Efficiency

There are a number of ways to improve the efficiency of algorithm (1),such as introducing approximations, using optimizers other than gradientdescent, etc. In one embodiment, the size of the kernel in K in equation(15) may be reduced and the gradient may be updated as specified in thefollowing example equation (20).

$\begin{matrix}{{\frac{\partial J}{\partial\varphi_{i}} = {C\left( {{2\; K\; \Phi_{i}} - {K\; \Phi_{i - 1}} - {K\; \Phi_{i + 1}}} \right)}},{{{where}\mspace{14mu} K} = \begin{bmatrix}{- 1} \\2 \\{- 1}\end{bmatrix}^{T}}} & (20)\end{matrix}$

By reducing the size of the kernel (and reusing it), the computation ofthe gradient may be effectively sped up. Another property of the kernelin equation (20) is that the value of Kφi may be computed moreaccurately using slerp. This may be done over non-uniformly spacedframes as specified in the following example equation (21).

$\begin{matrix}{{\partial\varphi_{i}} = {\varphi_{i} - {{slerp}\left( {\varphi_{i - 1},\varphi_{i + 1},\frac{t_{i} - t_{i - 1}}{t_{i + 1} - t_{i - 1}}} \right)}}} & (21)\end{matrix}$

Even more accurately, the spherical tangent formed by φi and slerp maybe determined and used in equation (20). The spherical tangent formed byφi and slerp may be specified in the following example expression.

$\varphi_{i}\mspace{14mu} {and}\mspace{14mu} {{slerp}\left( {\varphi_{i - 1},\varphi_{i + 1},\frac{t_{i} - t_{i - 1}}{t_{i + 1} - t_{i - 1}}} \right)}$

In another embodiment, efficiency may be improved by improving the rateof convergence of algorithm 1 described herein. This may be achieved byrunning it in coarse to fine mode. For example, algorithm 1 may beinitialized by supplying and solving for every 16th orientation φ_(i).Linear or cubic interpolation (e.g., slerp or squad) may then be used tocompute the φ_(i) in between. A value for every 8th orientation isobtained. Algorithm 1 may be run again, but now optimizing every 8thorientation for smoothness and constraints. This may be repeated untilalgorithm 1 has been run over every orientation.

Running coarse to fine may permit algorithm 1 to be run forsignificantly fewer iterations at each step. The overall camera motionmay be smoothed out and then the orientations may be refined to meetconstraints at increasingly smaller frame intervals while stillremaining smooth. In another embodiment, non-uniform sampling may beused. For example, instead of picking every 16th frame, frames may bepicked based on how far the orientation has deviated from the previouslypicked frame. The segments may then be subdivided until a smoothedorientation has been computed for all frames.

Since coarser or non-uniform sampling may introduce larger consecutivechanges in orientations, using the slerp modification presented inequation (21) may produce more accurate results.

Example Applications to Real-Time Stabilization

The following is provided as an example embodiment of adopting thealgorithm to real-time settings. With N frames kept in memory, thealgorithm is run in a sliding window fashion. Index i may denote thestart of the sliding window, and i+N may denote the end. Orientationsinside the sliding window may be malleable in that they may be updatedby running the algorithm. These orientations may be specified by thefollowing set (2).

{φ_(j)}_(j=i) ^(i+N)

Orientations preceding the sliding window (e.g., φ_(i−1)) may be fixed.The starting orientation may be φ_(i)−1 and the rate of rotation (e.g.,as measured by the gyroscope or computed from a feature tracker) may beintegrated to obtain orientations {θ_(i), θ_(i+)1, . . . , θ_(i+N)}.This may be used as input for the optimization algorithm and compute{φ_(i), φ_(i+1), . . . , φ_(i+N−)2}. The orientations {φ_(i−2), φ_(i−1)}and {φ_(i+N−1)=θ_(i+N−1), θ_(i+N)=θ_(i+N)} may be held fixed and mayserve as the boundary conditions that ensure that motions are smoothgoing into and out of the sliding window.

Once the algorithm is run, the orientation of φ_(i), which may be usedto warp frame F_(i), may be obtained. Once the frame has been warped, itmay be passed along to the encoder and removed from the buffer of Nframes. A new frame may then be received from the camera and the slidingwindow may be advanced by one frame.

The procedure may be repeated until the recording stops and all frameshave been processed. For the very first frame, i=1, {φ⁻¹, φ₀} may beundefined. φ⁻¹ and φ₀ may be set to the identity quaternion. Once thelast frame is received, the buffer may be flushed by using theorientations computed inside the final sliding window to warp theirrespective frames.

In some instances, a small buffer size (e.g., N=5) may not allow aneasing in and out of constraints. In such cases, it may be necessary tomodify the constraint function f to be a soft constraint that ramps upto a hard constraint. This may be referred to as function f′(φ, t).Instead of returning 0 or 1, f′ returns a new orientation φ′, that maybe pushed away from the frame border. The closer orientation φ comes toshowing an empty region, the more f′ may push the resulting φ′ away fromthe empty region. Algorithm 1 may then be reformulated as specified inthe following example algorithm (2).

Algorithm 2 Soft Constraint-Based Rotation Smoothing for i = 1..N doφ_(i) ← θ_(i) end for for j = 1..numiter do for i = 3..(N − 2) do φ_(i)← f′(n(φ_(i) − CKΦ_(i)), t_(i)) end for end for

Note that if f′ simply returns φ_(i) when orientation n(φ_(i)−CKφ_(i))results in empty regions, then algorithms 1 and 2 may be equivalent. Theoptimization rate of algorithm 1 may be improved by using algorithm 2,with a function f′ that slerps φi towards n(φ_(i)−CKφ_(i)) but stopsjust at the point where empty regions are about to appear.

Social Networking System—Example Implementation

FIG. 7 is a network diagram of an example system 700 for estimating userattention on a website or application in accordance with an embodimentof the invention. The system 700 includes one or more user devices 710,one or more external systems 720, a social networking system 730, and anetwork 750. In an embodiment, the social networking system discussed inconnection with the embodiments described above may be implemented asthe social networking system 730. For purposes of illustration, theembodiment of the system 700, shown by FIG. 7, includes a singleexternal system 720 and a single user device 710. However, in otherembodiments, the system 700 may include more user devices 710 and/ormore external systems 720. In certain embodiments, the social networkingsystem 730 is operated by a social network provider, whereas theexternal systems 720 are separate from the social networking system 730in that they may be operated by different entities. In variousembodiments, however, the social networking system 730 and the externalsystems 720 operate in conjunction to provide social networking servicesto users (or members) of the social networking system 730. In thissense, the social networking system 730 provides a platform or backbone,which other systems, such as external systems 720, may use to providesocial networking services and functionalities to users across theInternet.

The user device 710 comprises one or more computing devices that canreceive input from a user and transmit and receive data via the network750. In one embodiment, the user device 710 is a conventional computersystem executing, for example, a Microsoft Windows compatible operatingsystem (OS), Apple OS X, and/or a Linux distribution. In anotherembodiment, the user device 710 can be a device having computerfunctionality, such as a smart-phone, a tablet, a personal digitalassistant (PDA), a mobile telephone, etc. The user device 710 isconfigured to communicate via the network 750. The user device 710 canexecute an application, for example, a browser application that allows auser of the user device 710 to interact with the social networkingsystem 730. In another embodiment, the user device 710 interacts withthe social networking system 730 through an application programminginterface (API) provided by the native operating system of the userdevice 710, such as iOS and ANDROID. The user device 710 is configuredto communicate with the external system 720 and the social networkingsystem 730 via the network 750, which may comprise any combination oflocal area and/or wide area networks, using wired and/or wirelesscommunication systems.

In one embodiment, the network 750 uses standard communicationstechnologies and protocols. Thus, the network 750 can include linksusing technologies such as Ethernet, 802.11, worldwide interoperabilityfor microwave access (WiMAX), 3G, 4G, CDMA, GSM, LTE, digital subscriberline (DSL), etc. Similarly, the networking protocols used on the network750 can include multiprotocol label switching (MPLS), transmissioncontrol protocol/Internet protocol (TCP/IP), User Datagram Protocol(UDP), hypertext transport protocol (HTTP), simple mail transferprotocol (SMTP), file transfer protocol (FTP), and the like. The dataexchanged over the network 750 can be represented using technologiesand/or formats including hypertext markup language (HTML) and extensiblemarkup language (XML). In addition, all or some links can be encryptedusing conventional encryption technologies such as secure sockets layer(SSL), transport layer security (TLS), and Internet Protocol security(IPsec).

In one embodiment, the user device 710 may display content from theexternal system 720 and/or from the social networking system 730 byprocessing a markup language document 714 received from the externalsystem 720 and from the social networking system 730 using a browserapplication 712. The markup language document 714 identifies content andone or more instructions describing formatting or presentation of thecontent. By executing the instructions included in the markup languagedocument 714, the browser application 712 displays the identifiedcontent using the format or presentation described by the markuplanguage document 714. For example, the markup language document 714includes instructions for generating and displaying a web page havingmultiple frames that include text and/or image data retrieved from theexternal system 720 and the social networking system 730. In variousembodiments, the markup language document 714 comprises a data fileincluding extensible markup language (XML) data, extensible hypertextmarkup language (XHTML) data, or other markup language data.Additionally, the markup language document 714 may include JavaScriptObject Notation (JSON) data, JSON with padding (JSONP), and JavaScriptdata to facilitate data-interchange between the external system 720 andthe user device 710. The browser application 712 on the user device 710may use a JavaScript compiler to decode the markup language document714.

The markup language document 714 may also include, or link to,applications or application frameworks such as FLASH™ or Unity™applications, the SilverLight™ application framework, etc.

In one embodiment, the user device 710 also includes one or more cookies716 including data indicating whether a user of the user device 710 islogged into the social networking system 730, which may enablemodification of the data communicated from the social networking system730 to the user device 710.

The external system 720 includes one or more web servers that includeone or more web pages 722 a, 722 b, which are communicated to the userdevice 710 using the network 750. The external system 720 is separatefrom the social networking system 730. For example, the external system720 is associated with a first domain, while the social networkingsystem 730 is associated with a separate social networking domain. Webpages 722 a, 722 b, included in the external system 720, comprise markuplanguage documents 714 identifying content and including instructionsspecifying formatting or presentation of the identified content.

The social networking system 730 includes one or more computing devicesfor a social network, including a plurality of users, and providingusers of the social network with the ability to communicate and interactwith other users of the social network. In some instances, the socialnetwork can be represented by a graph, i.e., a data structure includingedges and nodes. Other data structures can also be used to represent thesocial network, including but not limited to databases, objects,classes, meta elements, files, or any other data structure. The socialnetworking system 730 may be administered, managed, or controlled by anoperator. The operator of the social networking system 730 may be ahuman being, an automated application, or a series of applications formanaging content, regulating policies, and collecting usage metricswithin the social networking system 730. Any type of operator may beused.

Users may join the social networking system 730 and then add connectionsto any number of other users of the social networking system 730 to whomthey desire to be connected. As used herein, the term “friend” refers toany other user of the social networking system 730 to whom a user hasformed a connection, association, or relationship via the socialnetworking system 730. For example, in an embodiment, if users in thesocial networking system 730 are represented as nodes in the socialgraph, the term “friend” can refer to an edge formed between anddirectly connecting two users.

Connections may be added explicitly by a user or may be automaticallycreated by the social networking system 730 based on commoncharacteristics of the users (e.g., users who are alumni of the sameeducational institution). For example, a first user specifically selectsa particular other user to be a friend. Connections in the socialnetworking system 730 are usually in both directions, but need not be,so the terms “user” and “friend” depend on the frame of reference.Connections between users of the social networking system 730 areusually bilateral (“two-way”), or “mutual,” but connections may also beunilateral, or “one-way.” For example, if Bob and Joe are both users ofthe social networking system 730 and connected to each other, Bob andJoe are each other's connections. If, on the other hand, Bob wishes toconnect to Joe to view data communicated to the social networking system730 by Joe, but Joe does not wish to form a mutual connection, aunilateral connection may be established. The connection between usersmay be a direct connection; however, some embodiments of the socialnetworking system 730 allow the connection to be indirect via one ormore levels of connections or degrees of separation.

In addition to establishing and maintaining connections between usersand allowing interactions between users, the social networking system730 provides users with the ability to take actions on various types ofitems supported by the social networking system 730. These items mayinclude groups or networks (i.e., social networks of people, entities,and concepts) to which users of the social networking system 730 maybelong, events or calendar entries in which a user might be interested,computer-based applications that a user may use via the socialnetworking system 730, transactions that allow users to buy or sellitems via services provided by or through the social networking system730, and interactions with advertisements that a user may perform on oroff the social networking system 730. These are just a few examples ofthe items upon which a user may act on the social networking system 730,and many others are possible. A user may interact with anything that iscapable of being represented in the social networking system 730 or inthe external system 720, separate from the social networking system 730,or coupled to the social networking system 730 via the network 750.

The social networking system 730 is also capable of linking a variety ofentities. For example, the social networking system 730 enables users tointeract with each other as well as external systems 720 or otherentities through an API, a web service, or other communication channels.The social networking system 730 generates and maintains the “socialgraph” comprising a plurality of nodes interconnected by a plurality ofedges. Each node in the social graph may represent an entity that canact on another node and/or that can be acted on by another node. Thesocial graph may include various types of nodes. Examples of types ofnodes include users, non-person entities, content items, web pages,groups, activities, messages, concepts, and any other things that can berepresented by an object in the social networking system 730. An edgebetween two nodes in the social graph may represent a particular kind ofconnection, or association, between the two nodes, which may result fromnode relationships or from an action that was performed by one of thenodes on the other node. In some cases, the edges between nodes can beweighted. The weight of an edge can represent an attribute associatedwith the edge, such as a strength of the connection or associationbetween nodes. Different types of edges can be provided with differentweights. For example, an edge created when one user “likes” another usermay be given one weight, while an edge created when a user befriendsanother user may be given a different weight.

As an example, when a first user identifies a second user as a friend,an edge in the social graph is generated connecting a node representingthe first user and a second node representing the second user. Asvarious nodes relate or interact with each other, the social networkingsystem 730 modifies edges connecting the various nodes to reflect therelationships and interactions.

The social networking system 730 also includes user-generated content,which enhances a user's interactions with the social networking system730. User-generated content may include anything a user can add, upload,send, or “post” to the social networking system 730. For example, a usercommunicates posts to the social networking system 730 from a userdevice 710. Posts may include data such as status updates or othertextual data, location information, images such as photos, videos,links, music or other similar data and/or media. Content may also beadded to the social networking system 730 by a third party. Content“items” are represented as objects in the social networking system 730.In this way, users of the social networking system 730 are encouraged tocommunicate with each other by posting text and content items of varioustypes of media through various communication channels. Suchcommunication increases the interaction of users with each other andincreases the frequency with which users interact with the socialnetworking system 730.

The social networking system 730 includes a web server 732, an APIrequest server 734, a user profile store 736, a connection store 738, anaction logger 740, an activity log 742, an authorization server 744, anda digital video stabilization module 746. In an embodiment of theinvention, the social networking system 730 may include additional,fewer, or different components for various applications. Othercomponents, such as network interfaces, security mechanisms, loadbalancers, failover servers, management and network operations consoles,and the like are not shown so as to not obscure the details of thesystem.

The user profile store 736 maintains information about user accounts,including biographic, demographic, and other types of descriptiveinformation, such as work experience, educational history, hobbies orpreferences, location, and the like that has been declared by users orinferred by the social networking system 730. This information is storedin the user profile store 736 such that each user is uniquelyidentified. The social networking system 730 also stores data describingone or more connections between different users in the connection store738. The connection information may indicate users who have similar orcommon work experience, group memberships, hobbies, or educationalhistory. Additionally, the social networking system 730 includesuser-defined connections between different users, allowing users tospecify their relationships with other users. For example, user-definedconnections allow users to generate relationships with other users thatparallel the users' real-life relationships, such as friends,co-workers, partners, and so forth. Users may select from predefinedtypes of connections, or define their own connection types as needed.Connections with other nodes in the social networking system 730, suchas non-person entities, buckets, cluster centers, images, interests,pages, external systems, concepts, and the like are also stored in theconnection store 738.

The social networking system 730 maintains data about objects with whicha user may interact. To maintain this data, the user profile store 736and the connection store 738 store instances of the corresponding typeof objects maintained by the social networking system 730. Each objecttype has information fields that are suitable for storing informationappropriate to the type of object. For example, the user profile store736 contains data structures with fields suitable for describing auser's account and information related to a user's account. When a newobject of a particular type is created, the social networking system 730initializes a new data structure of the corresponding type, assigns aunique object identifier to it, and begins to add data to the object asneeded. This might occur, for example, when a user becomes a user of thesocial networking system 730, the social networking system 730 generatesa new instance of a user profile in the user profile store 736, assignsa unique identifier to the user account, and begins to populate thefields of the user account with information provided by the user.

The connection store 738 includes data structures suitable fordescribing a user's connections to other users, connections to externalsystems 720 or connections to other entities. The connection store 738may also associate a connection type with a user's connections, whichmay be used in conjunction with the user's privacy setting to regulateaccess to information about the user. In an embodiment of the invention,the user profile store 736 and the connection store 738 may beimplemented as a federated database.

Data stored in the connection store 738, the user profile store 736, andthe activity log 742 enables the social networking system 730 togenerate the social graph that uses nodes to identify various objectsand edges connecting nodes to identify relationships between differentobjects. For example, if a first user establishes a connection with asecond user in the social networking system 730, user accounts of thefirst user and the second user from the user profile store 736 may actas nodes in the social graph. The connection between the first user andthe second user stored by the connection store 738 is an edge betweenthe nodes associated with the first user and the second user. Continuingthis example, the second user may then send the first user a messagewithin the social networking system 730. The action of sending themessage, which may be stored, is another edge between the two nodes inthe social graph representing the first user and the second user.Additionally, the message itself may be identified and included in thesocial graph as another node connected to the nodes representing thefirst user and the second user.

In another example, a first user may tag a second user in an image thatis maintained by the social networking system 730 (or, alternatively, inan image maintained by another system outside of the social networkingsystem 730). The image may itself be represented as a node in the socialnetworking system 730. This tagging action may create edges between thefirst user and the second user as well as create an edge between each ofthe users and the image, which is also a node in the social graph. Inyet another example, if a user confirms attending an event, the user andthe event are nodes obtained from the user profile store 736, where theattendance of the event is an edge between the nodes that may beretrieved from the activity log 742. By generating and maintaining thesocial graph, the social networking system 730 includes data describingmany different types of objects and the interactions and connectionsamong those objects, providing a rich source of socially relevantinformation.

The web server 732 links the social networking system 730 to one or moreuser devices 710 and/or one or more external systems 720 via the network750. The web server 732 serves web pages, as well as other web-relatedcontent, such as Java, JavaScript, Flash, XML, and so forth. The webserver 732 may include a mail server or other messaging functionalityfor receiving and routing messages between the social networking system730 and one or more user devices 710. The messages can be instantmessages, queued messages (e.g., email), text and SMS messages, or anyother suitable messaging format.

The API request server 734 allows one or more external systems 720 anduser devices 710 to call access information from the social networkingsystem 730 by calling one or more API functions. The API request server734 may also allow external systems 720 to send information to thesocial networking system 730 by calling APIs. The external system 720,in one embodiment, sends an API request to the social networking system730 via the network 750, and the API request server 734 receives the APIrequest. The API request server 734 processes the request by calling anAPI associated with the API request to generate an appropriate response,which the API request server 734 communicates to the external system 720via the network 750. For example, responsive to an API request, the APIrequest server 734 collects data associated with a user, such as theuser's connections that have logged into the external system 720, andcommunicates the collected data to the external system 720. In anotherembodiment, the user device 710 communicates with the social networkingsystem 730 via APIs in the same manner as external systems 720.

The action logger 740 is capable of receiving communications from theweb server 732 about user actions on and/or off the social networkingsystem 730. The action logger 740 populates the activity log 742 withinformation about user actions, enabling the social networking system730 to discover various actions taken by its users within the socialnetworking system 730 and outside of the social networking system 730.Any action that a particular user takes with respect to another node onthe social networking system 730 may be associated with each user'saccount, through information maintained in the activity log 742 or in asimilar database or other data repository. Examples of actions taken bya user within the social networking system 730 that are identified andstored may include, for example, adding a connection to another user,sending a message to another user, reading a message from another user,viewing content associated with another user, attending an event postedby another user, posting an image, attempting to post an image, or otheractions interacting with another user or another object. When a usertakes an action within the social networking system 730, the action isrecorded in the activity log 742. In one embodiment, the socialnetworking system 730 maintains the activity log 742 as a database ofentries. When an action is taken within the social networking system730, an entry for the action is added to the activity log 742. Theactivity log 742 may be referred to as an action log.

Additionally, user actions may be associated with concepts and actionsthat occur within an entity outside of the social networking system 730,such as an external system 720 that is separate from the socialnetworking system 730. For example, the action logger 740 may receivedata describing a user's interaction with an external system 720 fromthe web server 732. In this example, the external system 720 reports auser's interaction according to structured actions and objects in thesocial graph.

Other examples of actions where a user interacts with an external system720 include a user expressing an interest in an external system 720 oranother entity, a user posting a comment to the social networking system730 that discusses an external system 720 or a web page 722 a within theexternal system 720, a user posting to the social networking system 730a Uniform Resource Locator (URL) or other identifier associated with anexternal system 720, a user attending an event associated with anexternal system 720, or any other action by a user that is related to anexternal system 720. Thus, the activity log 742 may include actionsdescribing interactions between a user of the social networking system730 and an external system 720 that is separate from the socialnetworking system 730.

The authorization server 744 enforces one or more privacy settings ofthe users of the social networking system 730. A privacy setting of auser determines how particular information associated with a user can beshared. The privacy setting comprises the specification of particularinformation associated with a user and the specification of the entityor entities with whom the information can be shared. Examples ofentities with which information can be shared may include other users,applications, external systems 720, or any entity that can potentiallyaccess the information. The information that can be shared by a usercomprises user account information, such as profile photos, phonenumbers associated with the user, user's connections, actions taken bythe user such as adding a connection, changing user profile information,and the like.

The privacy setting specification may be provided at different levels ofgranularity. For example, the privacy setting may identify specificinformation to be shared with other users; the privacy settingidentifies a work phone number or a specific set of related information,such as, personal information including profile photo, home phonenumber, and status. Alternatively, the privacy setting may apply to allthe information associated with the user. The specification of the setof entities that can access particular information can also be specifiedat various levels of granularity. Various sets of entities with whichinformation can be shared may include, for example, all friends of theuser, all friends of friends, all applications, or all external systems720. One embodiment allows the specification of the set of entities tocomprise an enumeration of entities. For example, the user may provide alist of external systems 720 that are allowed to access certaininformation. Another embodiment allows the specification to comprise aset of entities along with exceptions that are not allowed to access theinformation. For example, a user may allow all external systems 720 toaccess the user's work information, but specify a list of externalsystems 720 that are not allowed to access the work information. Certainembodiments call the list of exceptions that are not allowed to accesscertain information a “block list”. External systems 720 belonging to ablock list specified by a user are blocked from accessing theinformation specified in the privacy setting. Various combinations ofgranularity of specification of information, and granularity ofspecification of entities, with which information is shared arepossible. For example, all personal information may be shared withfriends whereas all work information may be shared with friends offriends.

The authorization server 744 contains logic to determine if certaininformation associated with a user can be accessed by a user's friends,external systems 720, and/or other applications and entities. Theexternal system 720 may need authorization from the authorization server744 to access the user's more private and sensitive information, such asthe user's work phone number. Based on the user's privacy settings, theauthorization server 744 determines if another user, the external system720, an application, or another entity is allowed to access informationassociated with the user, including information about actions taken bythe user.

The social networking system 730 may include a digital videostabilization module 746. The digital video stabilization module 746 maycompute a set of smooth camera orientations under the constraint thatempty regions are not visible, or below a minimum threshold value. Thedigital video stabilization module 746 may then generate warped framesbased on the set of new smoothed camera orientations. In an embodiment,the digital video stabilization module 746 may be implemented as thedigital video stabilization 400 of FIG. 4.

Hardware Implementation

The foregoing processes and features can be implemented by a widevariety of machine and computer system architectures and in a widevariety of network and computing environments. FIG. 8 illustrates anexample of a computer system 800 that may be used to implement one ormore of the embodiments described herein in accordance with anembodiment of the invention. The computer system 800 includes sets ofinstructions for causing the computer system 800 to perform theprocesses and features discussed herein. The computer system 800 may beconnected (e.g., networked) to other machines. In a networkeddeployment, the computer system 800 may operate in the capacity of aserver machine or a client machine in a client-server networkenvironment, or as a peer machine in a peer-to-peer (or distributed)network environment. In an embodiment of the invention, the computersystem 800 may be a component of the social networking system describedherein. In an embodiment of the invention, the computer system 800 maybe one server among many that constitutes all or part of the socialnetworking system 830.

The computer system 800 includes a processor 802, a cache 804, and oneor more executable modules and drivers, stored on a computer-readablemedium, directed to the processes and features described herein.Additionally, the computer system 800 includes a high performanceinput/output (I/O) bus 806 and a standard I/O bus 808. A host bridge 810couples processor 802 to high performance I/O bus 806, whereas I/O busbridge 812 couples the two buses 806 and 808 to each other. A systemmemory 814 and one or more network interfaces 816 couple to highperformance I/O bus 806. The computer system 800 may further includevideo memory and a display device coupled to the video memory (notshown). Mass storage 818 and I/O ports 820 couple to the standard I/Obus 808. The computer system 800 may optionally include a keyboard andpointing device, a display device, or other input/output devices (notshown) coupled to the standard I/O bus 808. Collectively, these elementsare intended to represent a broad category of computer hardware systems,including but not limited to computer systems based on thex86-compatible processors manufactured by Intel Corporation of SantaClara, Calif., and the x86-compatible processors manufactured byAdvanced Micro Devices (AMD), Inc., of Sunnyvale, Calif., as well as anyother suitable processor.

An operating system manages and controls the operation of the computersystem 800, including the input and output of data to and from softwareapplications (not shown). The operating system provides an interfacebetween the software applications being executed on the system and thehardware components of the system. Any suitable operating system may beused, such as the LINUX Operating System, the Apple Macintosh OperatingSystem, available from Apple Computer Inc. of Cupertino, Calif., UNIXoperating systems, Microsoft® Windows® operating systems, BSD operatingsystems, and the like. Other implementations are possible.

The elements of the computer system 800 are described in greater detailbelow. In particular, the network interface 816 provides communicationbetween the computer system 800 and any of a wide range of networks,such as an Ethernet (e.g., IEEE 802.3) network, a backplane, etc. Themass storage 818 provides permanent storage for the data and programminginstructions to perform the above-described processes and featuresimplemented by the respective computing systems identified above,whereas the system memory 814 (e.g., DRAM) provides temporary storagefor the data and programming instructions when executed by the processor802. The I/O ports 820 may be one or more serial and/or parallelcommunication ports that provide communication between additionalperipheral devices, which may be coupled to the computer system 800.

The computer system 800 may include a variety of system architectures,and various components of the computer system 800 may be rearranged. Forexample, the cache 804 may be on-chip with processor 802. Alternatively,the cache 804 and the processor 802 may be packed together as a“processor module”, with processor 802 being referred to as the“processor core”. Furthermore, certain embodiments of the invention mayneither require nor include all of the above components. For example,peripheral devices coupled to the standard I/O bus 808 may couple to thehigh performance I/O bus 806. In addition, in some embodiments, only asingle bus may exist, with the components of the computer system 800being coupled to the single bus. Furthermore, the computer system 800may include additional components, such as additional processors,storage devices, or memories.

In general, the processes and features described herein may beimplemented as part of an operating system or a specific application,component, program, object, module, or series of instructions referredto as “programs”. For example, one or more programs may be used toexecute specific processes described herein. The programs typicallycomprise one or more instructions in various memory and storage devicesin the computer system 800 that, when read and executed by one or moreprocessors, cause the computer system 800 to perform operations toexecute the processes and features described herein. The processes andfeatures described herein may be implemented in software, firmware,hardware (e.g., an application specific integrated circuit), or anycombination thereof.

In one implementation, the processes and features described herein areimplemented as a series of executable modules run by the computer system800, individually or collectively in a distributed computingenvironment. The foregoing modules may be realized by hardware,executable modules stored on a computer-readable medium (ormachine-readable medium), or a combination of both. For example, themodules may comprise a plurality or series of instructions to beexecuted by a processor in a hardware system, such as the processor 802.Initially, the series of instructions may be stored on a storage device,such as the mass storage 818. However, the series of instructions can bestored on any suitable computer readable storage medium. Furthermore,the series of instructions need not be stored locally, and could bereceived from a remote storage device, such as a server on a network,via the network interface 816. The instructions are copied from thestorage device, such as the mass storage 818, into the system memory 814and then accessed and executed by the processor 802. In variousimplementations, a module or modules can be executed by a processor ormultiple processors in one or multiple locations, such as multipleservers in a parallel processing environment.

Examples of computer-readable media include, but are not limited to,recordable type media such as volatile and non-volatile memory devices;solid state memories; floppy and other removable disks; hard diskdrives; magnetic media; optical disks (e.g., Compact Disk Read-OnlyMemory (CD ROMS), Digital Versatile Disks (DVDs)); other similarnon-transitory (or transitory), tangible (or non-tangible) storagemedium; or any type of medium suitable for storing, encoding, orcarrying a series of instructions for execution by the computer system800 to perform any one or more of the processes and features describedherein.

For purposes of explanation, numerous specific details are set forth inorder to provide a thorough understanding of the description. It will beapparent, however, to one skilled in the art that embodiments of thedisclosure can be practiced without these specific details. In someinstances, modules, structures, processes, features, and devices areshown in block diagram form in order to avoid obscuring the description.In other instances, functional block diagrams and flow diagrams areshown to represent data and logic flows. The components of blockdiagrams and flow diagrams (e.g., modules, blocks, structures, devices,features, etc.) may be variously combined, separated, removed,reordered, and replaced in a manner other than as expressly describedand depicted herein.

Reference in this specification to “one embodiment”, “an embodiment”,“other embodiments”, “one series of embodiments”, “some embodiments”,“various embodiments”, or the like means that a particular feature,design, structure, or characteristic described in connection with theembodiment is included in at least one embodiment of the disclosure. Theappearances of, for example, the phrase “in one embodiment” or “in anembodiment” in various places in the specification are not necessarilyall referring to the same embodiment, nor are separate or alternativeembodiments mutually exclusive of other embodiments. Moreover, whetheror not there is express reference to an “embodiment” or the like,various features are described, which may be variously combined andincluded in some embodiments, but also variously omitted in otherembodiments. Similarly, various features are described that may bepreferences or requirements for some embodiments, but not otherembodiments.

The language used herein has been principally selected for readabilityand instructional purposes, and it may not have been selected todelineate or circumscribe the inventive subject matter. It is thereforeintended that the scope of the invention be limited not by this detaileddescription, but rather by any claims that issue on an application basedhereon. Accordingly, the disclosure of the embodiments of the inventionis intended to be illustrative, but not limiting, of the scope of theinvention, which is set forth in the following claims.

What is claimed:
 1. A computer-implemented method comprising: acquiring,by a computing system, video data comprising a set of image frameshaving associated time stamps; acquiring, by the computing system, a setof camera orientation data having associated time stamps, wherein theset of camera orientation data is based on an orientation of a camerawhile the video data is being acquired by the camera; and reorienting,by the computing system, each particular image frame in at least asubset of the set of image frames based on an associated subset of thecamera orientation data.
 2. The computer-implemented method of claim 1,wherein each particular image frame has a respective time stamp, andwherein the associated subset of the camera orientation data for eachparticular image frame also has the respective time stamp.
 3. Thecomputer-implemented method of claim 2, wherein each particular imageframe is reoriented based on rotating each particular image frame tocounteract undesired shaking indicated via the associated subset of thecamera orientation data for each particular image frame.
 4. The computerimplemented method of claim 3, wherein the undesired shaking indicatedvia the associated subset of the camera orientation data introducesdeformation to each particular image frame, and wherein each particularimage frame is rotated to counteract the deformation.
 5. Thecomputer-implemented method of claim 1, wherein reorienting eachparticular image frame in at least the subset of the set of image framesproduces a resulting set of smoothed image frames, and whereinreorienting each particular image frame in at least the subset of theset of image frames further comprises: minimizing a rate of rotationbetween each particular image frame and another image frame in at leastthe subset of the set of image frames while minimizing an amount ofempty regions in the resulting set of smoothed image frames.
 6. Thecomputer-implemented method of claim 5, wherein minimizing the amount ofempty regions in the resulting set of smoothed image frames furthercomprises: performing at least one of a cropping operation or a zoomingoperation with respect to each particular image frame in at least thesubset of the set of image frames.
 7. The computer-implemented method ofclaim 5, wherein each particular image frame and the other image framecorrespond to successive image frames.
 8. The computer-implementedmethod of claim 1, wherein the set of camera orientation data provides arepresentation of the orientation of the camera.
 9. Thecomputer-implemented method of claim 1, wherein the set of cameraorientation data is acquired by one or more orientation sensors, whereinthe one or more orientation sensors are included in the computingsystem, and wherein the computing system corresponds to at least one ofa computing device including the camera or a server remote from thecamera.
 10. The computer-implemented method of claim 9, wherein the oneor more orientation sensors include at least one of a gyroscope or anaccelerometer.
 11. A system comprising: at least one processor; and amemory storing instructions that, when executed by the at least oneprocessor, cause the system to perform: acquiring video data comprisinga set of image frames having associated time stamps; acquiring a set ofcamera orientation data having associated time stamps, wherein the setof camera orientation data is based on an orientation of a camera whilethe video data is being acquired by the camera; and reorienting eachparticular image frame in at least a subset of the set of image framesbased on an associated subset of the camera orientation data.
 12. Thesystem of claim 11, wherein each particular image frame has a respectivetime stamp, and wherein the associated subset of the camera orientationdata for each particular image frame also has the respective time stamp.13. The system of claim 12, wherein each particular image frame isreoriented based on rotating each particular image frame to counteractundesired shaking indicated via the associated subset of the cameraorientation data for each particular image frame.
 14. The system ofclaim 13, wherein the undesired shaking indicated via the associatedsubset of the camera orientation data introduces deformation to eachparticular image frame, and wherein each particular image frame isrotated to counteract the deformation.
 15. The system of claim 11,wherein reorienting each particular image frame in at least the subsetof the set of image frames produces a resulting set of smoothed imageframes, and wherein reorienting each particular image frame in at leastthe subset of the set of image frames further comprises: minimizing arate of rotation between each particular image frame and another imageframe in at least the subset of the set of image frames while minimizingan amount of empty regions in the resulting set of smoothed imageframes.
 16. A non-transitory computer-readable storage medium includinginstructions that, when executed by at least one processor of acomputing system, cause the computing system to perform a methodcomprising: acquiring video data comprising a set of image frames havingassociated time stamps; acquiring a set of camera orientation datahaving associated time stamps, wherein the set of camera orientationdata is based on an orientation of a camera while the video data isbeing acquired by the camera; and reorienting each particular imageframe in at least a subset of the set of image frames based on anassociated subset of the camera orientation data.
 17. The non-transitorycomputer-readable storage medium of claim 16, wherein each particularimage frame has a respective time stamp, and wherein the associatedsubset of the camera orientation data for each particular image framealso has the respective time stamp.
 18. The non-transitorycomputer-readable storage medium of claim 17, wherein each particularimage frame is reoriented based on rotating each particular image frameto counteract undesired shaking indicated via the associated subset ofthe camera orientation data for each particular image frame.
 19. Thenon-transitory computer-readable storage medium of claim 18, wherein theundesired shaking indicated via the associated subset of the cameraorientation data introduces deformation to each particular image frame,and wherein each particular image frame is rotated to counteract thedeformation.
 20. The non-transitory computer-readable storage medium ofclaim 16, wherein reorienting each particular image frame in at leastthe subset of the set of image frames produces a resulting set ofsmoothed image frames, and wherein reorienting each particular imageframe in at least the subset of the set of image frames furthercomprises: minimizing a rate of rotation between each particular imageframe and another image frame in at least the subset of the set of imageframes while minimizing an amount of empty regions in the resulting setof smoothed image frames.